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An increasing range of problems in Artificial Intelli- gence and Computer Science, such as autonomous vehi- cle control and planning with resources, are formulated through a combination of logical, algebraic and cost constraints. Their solution requires a hybrid mixture of logical decision techniques and mathematical opti- mization. Using Disjunctive Linear Programs (DLPs) to formulate these problems, we present a novel algo- rithm, called Generalized Conflict-Directed Branch and Bound (GCD-BB), that efficiently solves DLPs through a powerful three-fold method. First, during the search process, generalized conflict learning learns conflicts for regions of the state space that are infeasible or sub- optimal. Second, forward conflict-directed search uses these conflicts to guide the forward step of search, by moving away from regions of state space correspond- ing to known conflicts. Finally, induced unit clause relaxation automatically forms a strong relaxed prob- lem from a subset of the unit clauses that are implied by the original problem. Our experiments on model- based temporal plan execution for cooperative vehicles demonstrate an order of magnitude speed-up over Bi- nary Integer Programming Branch and Bound.

Generalized Conflict Learning for Hybrid Discrete/Linear Optimization